The Collatz conjecture is undecidable, so no Turing machine like you describe exists.
We don't know what specifically the deciding machine is, but it is either the one that always returns Yes or the one that returns whether or not x is below some finite value. Either case can be solved by only reading a bounded number of bits from the input.
With some work, one can eventually generalize Collatz to make an undecidable problem; this is more or less the basis for FRACTRAN. https://en.wikipedia.org/wiki/FRACTRAN